Page 171 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition
P. 171
Elementary Product Associated Permutation Even or Odd Signed Elementary Product
(1, 2) even
(2, 1) odd
(b)
Elementary Product Associated Permutation Even or Odd Signed Elementary Product
(1, 2, 3) even
(1, 3, 2) odd
(2, 1, 3) odd
(2, 3, 1) even
(3, 1, 2) even
(3, 2, 1) odd
We are now in a position to give the combinatorial definition of the determinant function.
DEFINITION to be the sum of all signed elementary products from .
Let A be a square matrix. We define
EXAMPLE 7 Determinants of and Matrices
Referring to Example 6, we obtain
(a)
(b)
Of course, this definition of agrees with the definition in Section 2.1, although we will not prove this.
